Q: Rough starts and engine dies at idle

My van has had trouble starting. When it starts, there's a rough idle, and while that's happening, the van usually dies if you try to put it in gear. Once you're moving, the problems disappear. Our van has a little over 100,000 miles on it, and has been pretty reliable. This starting issue only happens once a month or less. When it decides to have problems, they go away after one round of rough starts. I was thinking it might be the outside temperature at first, but there's no pattern. Tried changing to different grades of gas, but that didn't work either. This all started before the 100,000 mile mark, though we did have the normal things done at that time - timing belt and spark plugs. We've also changed the battery and tried using fuel additive to clean out the engine. No change. The rough starts feel like when you're missing a cylinder. When it happens, I can gun the engine without any issues, but when it drops back to idle, it dies. The biggest challenge is keeping it running long enough to get it moving. Since it isn't happening while the engine is warm or cold, I'm not sure what what else to do. Do I need to change my spark plugs and fuel filters? Anything else I should look at?